Problem: This problem is the most boring one you've ever seen. 

Given a sequence of integers a1, a2, ..., an and a non-negative integer h, our goal is to partition the sequence into two subsequences (not necessarily consist of continuous elements). Each element of the original sequence should be contained in exactly one of the result subsequences. Note, that one of the result subsequences can be empty.

Let's define function f(ai, aj) on pairs of distinct elements (that is i ≠ j) in the original sequence. If ai and aj are in the same subsequence in the current partition then f(ai, aj) = ai + aj otherwise f(ai, aj) = ai + aj + h. 

Consider all possible values of the function f for some partition. We'll call the goodness of this partiotion the difference between the maximum value of function f and the minimum value of function f.

Your task is to find a partition of the given sequence a that have the minimal possible goodness among all possible partitions.

Input

The first line of input contains integers n and h (2 ≤ n ≤ 105, 0 ≤ h ≤ 108). In the second line there is a list of n space-separated integers representing a1, a2, ..., an (0 ≤ ai ≤ 108).

Output

The first line of output should contain the required minimum goodness. 

The second line describes the optimal partition. You should print n whitespace-separated integers in the second line. The i-th integer is 1 if ai is in the first subsequence otherwise it should be 2.

If there are several possible correct answers you are allowed to print any of them.

Examples

Input

3 2
1 2 3


Output

1
1 2 2 


Input

5 10
0 1 0 2 1


Output

3
2 2 2 2 2 

Note

In the first sample the values of f are as follows: f(1, 2) = 1 + 2 + 2 = 5, f(1, 3) = 1 + 3 + 2 = 6 and f(2, 3) = 2 + 3 = 5. So the difference between maximum and minimum values of f is 1.

In the second sample the value of h is large, so it's better for one of the sub-sequences to be empty.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class B_Round_148_Div1 {

	public static long MOD = 1000000007;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		int h = in.nextInt();
		Point[] data = new Point[n];
		for (int i = 0; i < n; i++) {
			data[i] = new Point(i, in.nextInt());
		}
		Arrays.sort(data, new Comparator<Point>() {

			@Override
			public int compare(Point o1, Point o2) {

				return o1.y - o2.y;
			}
		});
		if (n <= 16) {
			int result = Integer.MAX_VALUE;
			int set = 0;
			for (int i = 0; i < 1 << n; i++) {
				int min = Integer.MAX_VALUE;
				int max = Integer.MIN_VALUE;
				for (int j = 0; j < n; j++) {
					for (int k = j + 1; k < n; k++) {
						int a = ((1 << j) & i) != 0 ? 1 : 0;
						int b = ((1 << k) & i) != 0 ? 1 : 0;
						int v;
						if (a == b) {
							v = data[j].y + data[k].y;
						} else {
							v = data[j].y + data[k].y + h;
						}
						if (min > v) {
							min = v;
						}
						if (max < v) {
							max = v;
						}
					}
				}
				if (max - min < result) {
					result = max - min;
					set = i;
				}
			}
			int[] re = new int[n];
			for (int i = 0; i < n; i++) {
				if (((1 << i) & set) != 0) {
					re[data[i].x] = 2;
				} else {
					re[data[i].x] = 1;
				}
			}
			out.println(result);
			for (int i : re) {
				out.print(i + " ");
			}
		} else {
			int min = data[0].y + data[1].y;
			int max = data[n - 1].y + data[n - 2].y;
			int result = max - min;
			min = Math.min(data[0].y + data[1].y + h, data[1].y + data[2].y);
			max = Math.max(data[n - 1].y + data[n - 2].y, data[n - 1].y
					+ data[0].y + h);
			if (result > max - min) {
				out.println(max - min);

				for (int i = 0; i < n; i++) {
					if (data[0].x != i)
						out.print(2 + " ");
					else
						out.print(1 + " ");
				}
			} else {
				out.println(result);
				for (int i = 0; i < n; i++) {
					out.print(2 + " ");
				}
			}
		}
		out.close();
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return x - o.x;
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}